As Section REF  discusses, the non-convex constraint () makes the problem difficult to solve. Hence, we propose solving (REF ) iteratively by fixing the rate expression with \(\tilde{R}_{u, q}\)  in (), and simultaneously updating \(\tilde{R}\)  and \(\beta \) . By doing so, () appears to be a weighted power constraint, which is quadratic (hence convex) in \(\mathbf {w}\)  [1]}. Given these points, we can express the sum-rate maximization problem as
\(\max _{\mathbf {w}, \mathbf {z}, \mathbf {r}} \quad & \sum _{ (u,q) } R_{u, q}  \\\textrm {s.t.}&~ (\ref {eq:rate}), (\ref {opt_ch3:const2}), (\ref {opt_ch3:const4})\\&\sum _{u \in \mathcal {U}} \tilde{R}_{u, q} \beta _{u,b,q} ||\mathbf {w}_{u,b,q}||_2^2 \le C_{b, q}.\) 
